Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 5x - 1$ and $ JT = 4x + 1$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {5x - 1} = {4x + 1}$ Solve for $x$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 5({2}) - 1$ $ JT = 4({2}) + 1$ $ CJ = 10 - 1$ $ JT = 8 + 1$ $ CJ = 9$ $ JT = 9$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {9} + {9}$ $ CT = 18$